Probability?

I have a conditional probability theory question:

Over the past years 40% of cameras sold have been of the basic model. Of those buying the basic model, 30% purchase an extended warranty, whereas 50% of all deluxe purchasers do so. If the user bought a an extended warranty, what is the probability that they have bought the basic model.

I figure i need P(Basic | warranty), which is

P(basic & warranty)/P(warranty)=P(Basic | Warranty)

the only problem is how to calculate P(warranty)
my thoughts are P(warranty) = P(Basic & warrenty) * P(basic)

Hi,

If 40% of cameras sold have been of the basic model, then 60% of the cameras sold were the deluxe model. If 100 total cameras were sold, then 40 were basic and 60 were deluxe.

Of those buying the basic model, 30% purchase an extended warranty, so 30% of 40 is 12 warranties purchased.

Of those buying the basic model, 50% purchase an extended warranty, so 50% of 60 is 30 warranties purchased.

That means 42 warranties were purchased and 12 of those were basic model customers. The probability of a warranty purchaser buying a basic camera was 12 out of 42 or a 28.57% probability (2 out of 7).

I hope that helps!! :-)

p(warranty|basic)*p(basic) = p(basic&warranty)
p(warranty|deluxe)*p(deluxe) = p(deluxe&warranty)

p(deluxe) = 1-p(basic)

I believe this is called the law of total probability:
p(warranty) = p(warranty|basic)*p(basic) + p(warranty|deluxe)*p(deluxe)

=>
p(warranty) = p(warranty&basic) + p(warranty&deluxe)

Is The probability of me giving a correct answer to this question a conditional probability?